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<a href="thin__structure__math_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/* -------------------------------------------------------------------------*</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">*                               SPHinXsys                                   *</span></div><div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">* --------------------------------------------------------------------------*</span></div><div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">* SPHinXsys (pronunciation: s&#39;finksis) is an acronym from Smoothed Particle *</span></div><div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">* Hydrodynamics for industrial compleX systems. It provides C++ APIs for    *</span></div><div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">* physical accurate simulation and aims to model coupled industrial dynamic *</span></div><div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">* systems including fluid, solid, multi-body dynamics and beyond with SPH   *</span></div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">* (smoothed particle hydrodynamics), a meshless computational method using  *</span></div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">* particle discretization.                                                  *</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">* SPHinXsys is partially funded by German Research Foundation               *</span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">* (Deutsche Forschungsgemeinschaft) DFG HU1527/6-1, HU1527/10-1             *</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">* and HU1527/12-1.                                                          *</span></div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">* Portions copyright (c) 2017-2020 Technical University of Munich and       *</span></div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">* the authors&#39; affiliations.                                                *</span></div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">* Licensed under the Apache License, Version 2.0 (the &quot;License&quot;); you may   *</span></div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">* not use this file except in compliance with the License. You may obtain a *</span></div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">* copy of the License at http://www.apache.org/licenses/LICENSE-2.0.        *</span></div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">*                                                                           *</span></div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">* --------------------------------------------------------------------------*/</span></div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#ifndef THIN_STRUCTURE_MATH_H</span></div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="preprocessor">#define THIN_STRUCTURE_MATH_H</span></div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">#include &quot;all_particle_dynamics.h&quot;</span></div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="elastic__solid_8h.html">elastic_solid.h</a>&quot;</span></div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="weakly__compressible__fluid_8h.html">weakly_compressible_fluid.h</a>&quot;</span></div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="base__kernel_8h.html">base_kernel.h</a>&quot;</span></div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespace_s_p_h.html">SPH</a></div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;{</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keyword">namespace </span>thin_structure_dynamics</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    {</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;        Vec2d <a class="code" href="thin__structure__math_8cpp.html#a25a33ee7e23ffafa90ab86955c394f90">getVectorAfterThinStructureRotation</a>(<span class="keyword">const</span> Vec2d &amp;initial_vector, <span class="keyword">const</span> Vec2d &amp;rotation_angles);</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        Vec3d <a class="code" href="thin__structure__math_8cpp.html#a25a33ee7e23ffafa90ab86955c394f90">getVectorAfterThinStructureRotation</a>(<span class="keyword">const</span> Vec3d &amp;initial_vector, <span class="keyword">const</span> Vec3d &amp;rotation_angles);</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        Vec2d <a class="code" href="thin__structure__math_8cpp.html#a367237431bca151646b6c5c810be8682">getVectorChangeRateAfterThinStructureRotation</a>(<span class="keyword">const</span> Vec2d &amp;initial_vector, <span class="keyword">const</span> Vec2d &amp;rotation_angles, <span class="keyword">const</span> Vec2d &amp;angular_vel);</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        Vec3d <a class="code" href="thin__structure__math_8cpp.html#a367237431bca151646b6c5c810be8682">getVectorChangeRateAfterThinStructureRotation</a>(<span class="keyword">const</span> Vec3d &amp;initial_vector, <span class="keyword">const</span> Vec3d &amp;rotation_angles, <span class="keyword">const</span> Vec3d &amp;angular_vel);</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        Vec2d <a class="code" href="thin__structure__math_8cpp.html#aa524ddbd5a6e463a2c81c3b4473d4ff6">getRotationFromPseudoNormalForFiniteDeformation</a>(<span class="keyword">const</span> Vec2d &amp;dpseudo_n_d2t, <span class="keyword">const</span> Vec2d &amp;rotation, <span class="keyword">const</span> Vec2d &amp;angular_vel, Real dt);</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        Vec3d <a class="code" href="thin__structure__math_8cpp.html#aa524ddbd5a6e463a2c81c3b4473d4ff6">getRotationFromPseudoNormalForFiniteDeformation</a>(<span class="keyword">const</span> Vec3d &amp;dpseudo_n_d2t, <span class="keyword">const</span> Vec3d &amp;rotation, <span class="keyword">const</span> Vec3d &amp;angular_vel, Real dt);</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        Vec2d <a class="code" href="thin__structure__math_8cpp.html#a8b3fd329962c0fd43d4877fc318b881e">getRotationFromPseudoNormalForSmallDeformation</a>(<span class="keyword">const</span> Vec2d &amp;dpseudo_n_d2t, <span class="keyword">const</span> Vec2d &amp;rotation, <span class="keyword">const</span> Vec2d &amp;angular_vel, Real dt);</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        Vec3d <a class="code" href="thin__structure__math_8cpp.html#a8b3fd329962c0fd43d4877fc318b881e">getRotationFromPseudoNormalForSmallDeformation</a>(<span class="keyword">const</span> Vec3d &amp;dpseudo_n_d2t, <span class="keyword">const</span> Vec3d &amp;rotation, <span class="keyword">const</span> Vec3d &amp;angular_vel, Real dt);</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        Vec2d <a class="code" href="thin__structure__math_8cpp.html#a517398477499c3fce7a47dffeab2e92d">getNormalFromDeformationGradientTensor</a>(<span class="keyword">const</span> Mat2d &amp;F);</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        Vec3d <a class="code" href="thin__structure__math_8cpp.html#a517398477499c3fce7a47dffeab2e92d">getNormalFromDeformationGradientTensor</a>(<span class="keyword">const</span> Mat3d &amp;F);</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <a class="code" href="class_vecd.html">Vecd</a> <a class="code" href="thin__structure__math_8cpp.html#a2f217f2b208ab1f336cc1b00723935d2">getLinearVariableJump</a>(<span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;e_ij, <span class="keyword">const</span> Real &amp;r_ij, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_i_value,</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            <span class="keyword">const</span> Matd &amp;gradient_particle_i_value, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_j_value, <span class="keyword">const</span> Matd &amp;gradient_particle_j_value);</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        <a class="code" href="class_vecd.html">Vecd</a> getWENOVariableJump(<span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;e_ij, <span class="keyword">const</span> Real &amp;r_ij, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_i_value,</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            <span class="keyword">const</span> Matd &amp;gradient_particle_i_value, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_j_value, <span class="keyword">const</span> Matd &amp;gradient_particle_j_value);</div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        <a class="code" href="class_vecd.html">Vecd</a> <a class="code" href="thin__structure__math_8cpp.html#aa53a80b9e112974841818c57f14bf565">getWENOStateWithStencilPoints</a>(<span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;v1, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;v2, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;v3, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;v4);</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <a class="code" href="class_vecd.html">Vecd</a> getWENOLeftState(<span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;e_ij, <span class="keyword">const</span> Real &amp;r_ij, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_i_value,</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            <span class="keyword">const</span> Matd &amp;gradient_particle_i_value, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_j_value, <span class="keyword">const</span> Matd &amp;gradient_particle_j_value);</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        <a class="code" href="class_vecd.html">Vecd</a> getWENORightState(<span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;e_ij, <span class="keyword">const</span> Real &amp;r_ij, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_i_value,</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            <span class="keyword">const</span> Matd &amp;gradient_particle_i_value, <span class="keyword">const</span> <a class="code" href="class_vecd.html">Vecd</a> &amp;particle_j_value, <span class="keyword">const</span> Matd &amp;gradient_particle_j_value);</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        Vec2d <a class="code" href="thin__structure__math_8cpp.html#ac40bea3e1f1e143b34aa507fefc5536c">getRotationJump</a>(<span class="keyword">const</span> Vec2d &amp;pseudo_n_jump, <span class="keyword">const</span> Mat2d &amp;transformation_matrix);</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        Vec3d <a class="code" href="thin__structure__math_8cpp.html#ac40bea3e1f1e143b34aa507fefc5536c">getRotationJump</a>(<span class="keyword">const</span> Vec3d &amp;pseudo_n_jump, <span class="keyword">const</span> Mat3d &amp;transformation_matrix);</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        Mat2d <a class="code" href="thin__structure__math_8cpp.html#a8de94c902e1d07ef64a3ade158d91cc2">getCorrectedAlmansiStrain</a>(<span class="keyword">const</span> Mat2d &amp;current_local_almansi_strain, <span class="keyword">const</span> Real &amp;nu_);</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;        Mat3d <a class="code" href="thin__structure__math_8cpp.html#a8de94c902e1d07ef64a3ade158d91cc2">getCorrectedAlmansiStrain</a>(<span class="keyword">const</span> Mat3d &amp;current_local_almansi_strain, <span class="keyword">const</span> Real &amp;nu_);</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    }</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;}</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="preprocessor">#endif //THIN_STRUCTURE_MATH_H</span></div><div class="ttc" id="thin__structure__math_8cpp_html_a517398477499c3fce7a47dffeab2e92d"><div class="ttname"><a href="thin__structure__math_8cpp.html#a517398477499c3fce7a47dffeab2e92d">SPH::thin_structure_dynamics::getNormalFromDeformationGradientTensor</a></div><div class="ttdeci">Vec2d getNormalFromDeformationGradientTensor(const Mat2d &amp;F)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:133</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_aa524ddbd5a6e463a2c81c3b4473d4ff6"><div class="ttname"><a href="thin__structure__math_8cpp.html#aa524ddbd5a6e463a2c81c3b4473d4ff6">SPH::thin_structure_dynamics::getRotationFromPseudoNormalForFiniteDeformation</a></div><div class="ttdeci">Vec2d getRotationFromPseudoNormalForFiniteDeformation(const Vec2d &amp;dpseudo_n_d2t, const Vec2d &amp;rotation, const Vec2d &amp;angular_vel, Real dt)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:93</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_aa53a80b9e112974841818c57f14bf565"><div class="ttname"><a href="thin__structure__math_8cpp.html#aa53a80b9e112974841818c57f14bf565">SPH::thin_structure_dynamics::getWENOStateWithStencilPoints</a></div><div class="ttdeci">Vecd getWENOStateWithStencilPoints(const Vecd &amp;v1, const Vecd &amp;v2, const Vecd &amp;v3, const Vecd &amp;v4)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:163</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_a8de94c902e1d07ef64a3ade158d91cc2"><div class="ttname"><a href="thin__structure__math_8cpp.html#a8de94c902e1d07ef64a3ade158d91cc2">SPH::thin_structure_dynamics::getCorrectedAlmansiStrain</a></div><div class="ttdeci">Mat2d getCorrectedAlmansiStrain(const Mat2d &amp;current_local_almansi_strain, const Real &amp;nu_)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:231</div></div>
<div class="ttc" id="class_vecd_html"><div class="ttname"><a href="class_vecd.html">Vecd</a></div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_a25a33ee7e23ffafa90ab86955c394f90"><div class="ttname"><a href="thin__structure__math_8cpp.html#a25a33ee7e23ffafa90ab86955c394f90">SPH::thin_structure_dynamics::getVectorAfterThinStructureRotation</a></div><div class="ttdeci">Vec2d getVectorAfterThinStructureRotation(const Vec2d &amp;initial_vector, const Vec2d &amp;rotation_angles)</div><div class="ttdoc">Each of these basic vector rotations appears counterclockwise. </div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:16</div></div>
<div class="ttc" id="base__kernel_8h_html"><div class="ttname"><a href="base__kernel_8h.html">base_kernel.h</a></div><div class="ttdoc">This is the base classes of kernel functions. Implementation will be implemented in derived classes...</div></div>
<div class="ttc" id="weakly__compressible__fluid_8h_html"><div class="ttname"><a href="weakly__compressible__fluid_8h.html">weakly_compressible_fluid.h</a></div><div class="ttdoc">Describe the weakly compressible fluid which is used model incompressible fluids. Here...</div></div>
<div class="ttc" id="elastic__solid_8h_html"><div class="ttname"><a href="elastic__solid_8h.html">elastic_solid.h</a></div><div class="ttdoc">These are classes for define properties of elastic solid materials. These classes are based on isotro...</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_a2f217f2b208ab1f336cc1b00723935d2"><div class="ttname"><a href="thin__structure__math_8cpp.html#a2f217f2b208ab1f336cc1b00723935d2">SPH::thin_structure_dynamics::getLinearVariableJump</a></div><div class="ttdeci">Vecd getLinearVariableJump(const Vecd &amp;e_ij, const Real &amp;r_ij, const Vecd &amp;particle_i_value, const Matd &amp;gradient_particle_i_value, const Vecd &amp;particle_j_value, const Matd &amp;gradient_particle_j_value)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:147</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_ac40bea3e1f1e143b34aa507fefc5536c"><div class="ttname"><a href="thin__structure__math_8cpp.html#ac40bea3e1f1e143b34aa507fefc5536c">SPH::thin_structure_dynamics::getRotationJump</a></div><div class="ttdeci">Vec2d getRotationJump(const Vec2d &amp;pseudo_n_jump, const Mat2d &amp;transformation_matrix)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:214</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_a8b3fd329962c0fd43d4877fc318b881e"><div class="ttname"><a href="thin__structure__math_8cpp.html#a8b3fd329962c0fd43d4877fc318b881e">SPH::thin_structure_dynamics::getRotationFromPseudoNormalForSmallDeformation</a></div><div class="ttdeci">Vec2d getRotationFromPseudoNormalForSmallDeformation(const Vec2d &amp;dpseudo_n_d2t, const Vec2d &amp;rotation, const Vec2d &amp;angular_vel, Real dt)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:118</div></div>
<div class="ttc" id="thin__structure__math_8cpp_html_a367237431bca151646b6c5c810be8682"><div class="ttname"><a href="thin__structure__math_8cpp.html#a367237431bca151646b6c5c810be8682">SPH::thin_structure_dynamics::getVectorChangeRateAfterThinStructureRotation</a></div><div class="ttdeci">Vec2d getVectorChangeRateAfterThinStructureRotation(const Vec2d &amp;initial_vector, const Vec2d &amp;rotation_angles, const Vec2d &amp;angular_vel)</div><div class="ttdef"><b>Definition:</b> thin_structure_math.cpp:48</div></div>
<div class="ttc" id="namespace_s_p_h_html"><div class="ttname"><a href="namespace_s_p_h.html">SPH</a></div><div class="ttdef"><b>Definition:</b> solid_body_supplementary.cpp:9</div></div>
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